Inverse imaging problems like denoising, interpolation and bit-depth enhancement are inherently ill-posed, and signal priors are often used for regularization. A recent popular prior is the graph-signal smoothness prior: a desired image patch-interpreted as a graph-signal on an appropriately chosen graph-is assumed to be smooth with respect to the underlying graph. In this talk, I will first explain why such a signal prior is sensible from a graph signal processing (GSP) perspective. Then, I will describe a new graph-signal smoothness prior called LERaG based on left eigenvectors of the random walk graph Laplacian matrix, which has many desirable image filtering properties yet is computation-efficient. Finally, I will describe how LERaG can be used for soft decoding of JPEG images, resulting in state-of-the-art restored image quality.